Neural RDEs extend CDEs to irregular time series.
problem Modeling long irregular time series efficiently.
method Representing time series through log-signature and solving RDEs.
result Significant training speed-ups and improved model performance.
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48 results for “Neural CDEs”
Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network based CDE models can suffer from severe over-fitting when trained with the maximum …
The vast majority of the neural network literature focuses on predicting point values for a given set of response variables, conditioned on a feature vector. In many cases we need to model the full joint conditional distribution over the response variables rather than simply making point predictions. In this paper, we …
AP-CDE uses NF to estimate high-dimensional conditional densities, improving interpretability.
problem Estimating conditional densities for high-dimensional responses like images.
method Extends NF neural networks to handle high-dimensional with a latent .
result Improves interpretation of latent components, especially .
We show a connection between the inequality and the inequality. In particular, we introduce a inequality as a slight generalization of which turns out to be equivalent to with appropriate choices of and . We use this to prove that the inequality implies the c…
Tabular foundation models outperform other methods in conditional density estimation across various datasets.
problem Estimating the full conditional distribution of a response given tabular covariates, especially in settings with heteroscedasticity, multimodality, or asymmetric uncertainty.
method Benchmarked three tabular foundation model variants (TabPFN and TabICL) against six CDE baselines on 39 real-world datasets.
result Tabular foundation models achieve the best CDE loss, log-likelihood, and CRPS across all sample sizes, outperforming other methods.
DCDC calculates convergence rates for Markov chains using neural networks.
problem Computing precise convergence rates for Markov chains is hard.
method Developed a neural network-based algorithm (DCDC) to bound convergence rates in Wasserstein distance.
result Demonstrated effective convergence bounds for real-world Markov chains.
Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challeng…
New method corrects ML for informative sampling in time-series treatment outcomes.
problem Informative sampling in irregularly observed data hinders accurate treatment outcome forecasting.
method Formalized as covariate shift, proposed inverse intensity-weighting framework, TESAR-CDE.
result TESAR-CDE effectively learns treatment outcomes under informative sampling.
In this paper,we will give an easy example to satisfy that we can not conclude CDE' Inequality just from the CD Inequality.
The CD inequalities and CDE inequalities are useful in the estimate of curvature on graphs. This article is based on the ufinite graph with large girth, and finally concludes some curvature estimate in CD and CDE.
Neural CDEs correct errors in learned time-series models for better forecasting.
problem Error accumulation in multi-step forecasts of learned time-series models.
method Predictor-Corrector framework with a neural controlled differential equation.
result The proposed framework consistently improves forecasting performance across various models.
It is well known in astronomy that propagating non-Gaussian prediction uncertainty in photometric redshift estimates is key to reducing bias in downstream cosmological analyses. Similarly, likelihood-free inference approaches, which are beginning to emerge as a tool for cosmological analysis, require a characterization…
On the Generalization and Approximation Capacities of Neural Controlled Differential Equationsstat.ML
NCDEs improve predictions for irregular time series data.
problem Theoretical understanding of NCDEs' performance and irregular time series effects.
method Combining CDE theory and neural net complexity measures.
result Generalization bound and detailed sampling and approximation bias analysis.
Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottleneck in some a…
Objective: To evaluate unsupervised clustering methods for identifying individual-level behavioral-clinical phenotypes that relate personal biomarkers and behavioral traits in type 2 diabetes (T2DM) self-monitoring data. Materials and Methods: We used hierarchical clustering (HC) to identify groups of meals with simila…
Framework combines random features with CDEs for efficient time-series learning.
problem Efficient training of time-series models with strong inductive bias.
method Random Fourier CDEs and Random Rough DEs using continuous-time reservoirs and log-ODE discretization.
result Unified perspective on random-feature reservoirs and path-signature theory.
Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equationscs.LG
A new method models continuous-time counterfactual outcomes using neural controlled differential equations.
problem Estimating personalized healthcare outcomes over irregularly sampled data.
method Interpreting data as samples from a continuous-time process, modeling latent trajectory using controlled differential equations, and using adversarial training for time-dependent confounding.
result TE-CDE consistently outperforms existing approaches in irregularly sampled scenarios.
DDN models flexible free-form conditional distributions.
problem Difficulty in explicitly approximating arbitrary conditional distributions.
method Deconvolutional neural network framework for discretizing continuous domains.
result DDN outperforms other density-estimation methods on various tasks.
We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver precise estimates in test datasets under prior probability and more general dataset…
MSLs use parallelizable root-finding for efficient ODE and PDE solutions.
problem Efficiently solving initial value problems for ODEs and PDEs.
method Leveraging time-parallel methods, MSLs use parallelizable root-finding algorithms.
result MSLs offer significant speedups in NFEs and inference time.
Recent exploration of optimal individualized decision rules (IDRs) for patients in precision medicine has attracted a lot of attention due to the heterogeneous responses of patients to different treatments. In the existing literature of precision medicine, an optimal IDR is defined as a decision function mapping from t…
Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model complexity, representational capacity and overfitting. In this work, we propose …
New fairness approach removes direct effects of unprivileged groups through causal regularization.
problem Ensuring fairness in machine learning models for unprivileged groups.
method Proposes a new fairness definition based on causal effects and develops regularizations to remove the impact of unprivileged groups on model outcomes.
result Demonstrates effectiveness of the approach on various datasets, reducing unfairness with minimal performance loss.
We study some equivalent properties of the curvature-dimension conditions inequality on infinite, but locally finite graph. These equivalences are gradient estimate, Poincaré type inequalities and reverse Poincaré inequalities. And we also obtain one equivalent property of gradient estimate for a new notion o…
In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature-dimension inequality , which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, hea…
In this paper, we prove the equivalent of ultracontractive bound of heat semigroup or the uniform upper bound of the heat kernel with the Nash inequality, Log-Sobolev inequalities on graphs. We also show that under the assumption of volume growth and nonnegative curvature the Sobolev inequality, Nash inequa…
LADaR framework calibrates machine learning models for instance-wise predictions.
problem Challenges in assessing and calibrating predictive distributions for complex inputs.
method Local Amortized Diagnostics and Reshaping of Conditional Densities (LADaR) framework and algorithm.
result Achieves better instance-wise calibration than existing methods in galaxy distance estimation.
There is a growing demand for nonparametric conditional density estimators (CDEs) in fields such as astronomy and economics. In astronomy, for example, one can dramatically improve estimates of the parameters that dictate the evolution of the Universe by working with full conditional densities instead of regression (i.…
FlexCodeTS is a flexible time series density estimator.
problem Estimating conditional densities for time series data.
method Nonparametric conditional density estimator based on arbitrary regression methods.
result FlexCodeTS adapts its convergence rate based on the chosen regression method.
Regression, unlike classification, has lacked a comprehensive and effective approach to deal with cost-sensitive problems by the reuse (and not a re-training) of general regression models. In this paper, a wide variety of cost-sensitive problems in regression (such as bids, asymmetric losses and rejection rules) can be…
By studying the heat semigroup, we prove Li-Yau type estimates for bounded and positive solutions of the heat equation on graphs, under the assumption of the curvature-dimension inequality , which can be consider as a notion of curvature for graphs. Furthermore, we derive that if a graph has non-negative cur…
Method learns dynamics from sparse, irregular feature data.
problem Learn system dynamics from sparse, irregularly sampled feature time series.
method Formulates as high-dimensional linear regression using signatures.
result Oracle bound on prediction error with explicit sampling dependencies.
Bayesian model selection improves multivariate causal discovery without restrictive assumptions.
problem Real-world causal discovery requires flexible assumptions to avoid restrictive model assumptions.
method Continuous relaxation of discrete model selection problem, using Causal Gaussian Process Conditional Density Estimator (CGP-CDE).
result Bayesian approach outperforms traditional methods in multivariate causal discovery.
Efficiently computes sparse signature coefficients using kernels.
problem Lack of efficient methods for sparse signature coefficients.
method Signature kernels and PDE-based methods.
result Sparse groups of signature coefficients can be isolated effectively.
Graphs of neural networks are represented to preserve symmetry, improving performance across various tasks.
problem Lack of equivariance in neural network representations of other neural networks.
method Represent neural networks as computational graphs and use graph neural networks to preserve permutation symmetry.
result Single model encodes diverse neural architectures, outperforming state-of-the-art methods.
Convolutional Neural Processes improve data efficiency in neural processes.
problem Improving data efficiency in neural processes for small datasets.
method Convolutional Neural Processes (ConvNPs) improve data efficiency by leveraging translation equivariance and convolutional neural networks.
result ConvNPs enhance the performance of neural processes in small-data problems.
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous ne…
Investigates how neural network graph structure impacts predictive performance.
problem Lack of understanding between neural network graph structure and predictive performance.
method Developed relational graph representation to analyze neural networks, identifying a 'sweet spot' for improved performance.
result Identified a 'sweet spot' in relational graph structure that significantly improves neural network predictive performance.
Novel framework explains generalization in deep neural networks.
problem Understanding and improving generalization in deep neural networks.
method Topological Quantum Neural Networks as the semi-classical limit of Deep Neural Networks.
result Demonstrates that the perceptron, viewed as the semi-classical limit, achieves similar results to standard neural networks without training.
Neural networks can approximate functions uniformly across various measures.
problem Universal approximation of functions across different probability measures.
method Proving neural networks are dense in Orlicz spaces, extending classical theorems.
result Neural networks uniformly approximate functions for weakly compact families of measures.
Investigates neural codes and their embeddings, proving conjectures and introducing new code types.
problem Analyzing neural codes and their embedding dimensions.
method Combinatorial, topological, and algebraic analysis; proving conjectures; introducing new neural code types.
result Proves conjectures about neural codes and their embeddings, introduces new code types.
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we present a compact neural circuit for two common numerical integrators: the explicit …
Quadratic models explain neural network behavior during training.
problem Understanding neural network dynamics during training with large learning rates.
method Developed and tested Neural Quadratic Models.
result Neural Quadratic Models exhibit the 'catapult phase' similar to neural networks.
Graph Metanetworks process diverse neural architectures efficiently.
problem Processing diverse neural architectures efficiently.
method Builds metanetworks using graph neural networks to process graphs representing input neural networks.
result Proves GMNs are expressive and equivariant to parameter permutation symmetries.
Optimal rates for shallow ReLU networks in nonparametric regression.
problem Approximating smooth and non-smooth functions with shallow ReLU networks.
method Analysis of shallow ReLU neural networks, using variation norms and deep learning theory.
result Optimal approximation rates for shallow ReLU networks in nonparametric regression.
New metric compares noisy neural trajectories using optimal transport.
problem Existing metrics fail to capture differences in noisy, dynamic neural responses.
method Proposed an optimal transport distance metric for Gaussian processes.
result Metric effectively compares neural dynamics in different systems.
The neural tangent kernel equivalence theorem fails in practice.
problem Does the neural tangent kernel (NTK) equivalence theorem hold in practical neural network training?
method Rigorously derived NTK and conducted numerical experiments to evaluate the equivalence theorem.
result Adding a layer to a neural network and the corresponding updated NTK do not yield matching changes in predictor error.